Mathematical Concepts

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Obj #
 Unit
 Objective:
"The learner will . . ."
 Standard(s)
 No. of Days
 Vocabulary Terms
 Resources
 Student Learning Activities
 Assessment

1
 Simplify exponential expressions
 12.1.3.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Compute accurately with real numbers
 12.1.3.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Estimate answers
 12.1.4
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b





2
 Apply geometric properties to solve problems (e.g., parallel lines, line transversals, similar triangles, congruent triangles, proportions)
 12.2.1.d
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Identify and apply right triangle relationships (e.g., sine, cosine, tangent, special right triangles, converse of Pythagorean Theorem)
 12.2.1.e
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Know the definitions and basic properties of a circle and use them to prove basic theorems and solve problems
 12.2.1.g
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Use coordinate geometry to analyze geometric situations (e.g., parallel lines, perpendicular lines, circle equations)
 12.2.2.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Apply the midpoint formula
 12.2.2.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Apply the distance formula
 12.2.2.c
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Explain and justify the effects of simple transformations on the ordered pairs of two-dimensional shapes
 12.2.3.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Use geometric models to visualize, describe, and solve problems (e.g., find the height of a tree; find the amount of paint needed for a room; scale model)
 12.2.4.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Use strategies to find surface area and volume of complex objects
 12.2.5.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Apply appropriate units and scales to solve problems involving measurement
 12.2.5.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Convert between various units of area and volume, such as square feet to square yards
 12.2.5.c
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Convert equivalent rates (e.g., feet/second to miles/hour)
 12.2.5.d
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Determine surface area and volume of three-dimensional objects (e.g., spheres, cones, pyramids)
 12.2.5.f
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b





3
 Represent, interpret, and analyze functions with graphs, tables, and algebraic notation and convert among these representations (e.g., linear, non-linear)
 12.3.1.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Identify domain and range of functions represented in either symbolic or graphical form(e.g., linear, non-linear)
 12.3.1.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Identify the slope and intercepts of a linear relationship from an equation or graph
 12.3.1.c
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Identify characteristics of linear and non-linear functions
 12.3.1.d
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Graph linear and non-linear functions
 12.3.1.e
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Compare and analyze the rate of change by using ordered pairs, tables, graphs, and equations
 12.3.1.f
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Model contextualized problems using various representations (e.g., graphs, tables, one variable equalities, one variable inequalities, linear equations in slope intercept form, inequalities in slope intercept form, system of linear equations with two variables)
 12.3.2.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Represent a variety of quantitative relationships using linear equations and one variable inequalities
 12.3.2.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Model contextualized problems using various representations for non-linear functions (e.g., quadratic, exponential, square root, and absolute value)
 12.3.2.d
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Simplify algebraic expressions involving exponents (e.g., (3x4)2)
 12.3.3.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Add and subtract polynomials
 12.3.3.c
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Multiply and divide polynomials (e.g., divide x3 – 8 by x – 2, divide x4 – 5x3 – 2x by x2)
 12.3.3.d
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Factor polynomials
 12.3.3.e
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Identify and generate equivalent forms of linear equations
 12.3.3.f
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Solve linear equations and inequalities including absolute value
 12.3.3.g
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Add, subtract, and simplify rational expressions
 12.3.3.j
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Multiply, divide, and simplify rational expressions
 12.3.3.k
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Combine functions by composition, as well as by addition, subtraction, multiplication, and division
 12.3.3.n
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b





4
 Interpret data represented by the normal distribution and formulate conclusions
 12.4.1.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Compute, identify, and interpret measures of central tendency (mean, median, mode) when provided a graph or data set
 12.4.1.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Explain how sample size and transformations of data affect measures of central tendency
 12.4.1.c
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Describe the shape and determine spread (variance, standard deviation) and outliers of a data set
 12.4.1.d
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Construct a sample space and a probability distribution
 12.4.3.a
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Identify dependent and independent events and calculate their probabilities
 12.4.3.b
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Use the appropriate counting techniques to determine the probability of an event (e.g., combinations, permutations)
 12.4.3.c
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b






Analyze events to determine if they are mutually exclusive
 12.4.3.d
LA 12.4.1.a
LA 12.4.1.c
LA 12.4.2.b